The principal valueof the logarithmic function of a complex variable is defined to ave its argument in the range -pi < arg(z) < pi. By writing z = tan(w) in terms of exponentials, show that:
tan-1(z) = (1/2i)ln[(1 + iz)/(1 - iz)]
The Attempt at a Solution
I have absolutely no idea where to start on this problem. My brain must be fried this week, but all I know how to do is write z = tan(w) in terms of exponentials.
z = (1/2i)(eiw + e-iw)/(eiw - eiw)